Share

# F ( X ) = 2 X − 2 X 2 , X > 0 - CBSE (Arts) Class 12 - Mathematics

#### Question

f(x) = 2/x - 2/x^2,  x>0

#### Solution

$\text { Given }: f\left( x \right) = \frac{2}{x} - \frac{2}{x^2} = 2 x^{- 1} - 2 x^{- 2}$

$\Rightarrow f'\left( x \right) = - 2 x^{- 2} + 4 x^{- 3} = \frac{4}{x^3} - \frac{2}{x^2}$

$\text { For the local maxima or minima, we must have }$

$f'\left( x \right) = 0$

$\Rightarrow \frac{4}{x^3} - \frac{2}{x^2} = 0$

$\Rightarrow 4 - 2x = 0$

$\Rightarrow x = 2$

$\text { Thus, x = 2 is the possible point of local maxima or local minima }.$

$\text { Now,}$

$f''\left( x \right) = \frac{- 12}{x^4} + \frac{4}{x^3}$

$\text { At }x = 2:$

$f''\left( 2 \right) = \frac{- 12}{16} + \frac{4}{8} = \frac{- 12 + 8}{16} = \frac{- 1}{4} < 0$

$\text { So, x = 2 is the point of local maximum }.$

$\text { The local maximum value is given by }$

$f\left( 2 \right) = \frac{2}{2} - \frac{2}{2^2} = 1 - \frac{1}{2} = \frac{1}{2}$

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution F ( X ) = 2 X − 2 X 2 , X > 0 Concept: Graph of Maxima and Minima.
S